Question

1. how has polygon a been transformed to polygon b? dilate by a scale factor of 2 and move down reflect horizontally and then reflect vertically translate 5 units right and 4 units down rotate 180 degrees and then reflect vertically

Explanation:

Step1: Analyze translation

Translation involves moving a figure without rotation or reflection.
For horizontal movement: If we consider a point on polygon A, say \((- 2,0)\). After translation, if we assume translation \(x\) units right and \(y\) units down.
For vertical movement:
If we check the \(x\) - coordinate: from \(x=-2\) (for a point on A) to \(x = 3\) (approximate for a corresponding point on B), the change in \(x\) is \(3-(-2)=5\) units right.
If we check the \(y\) - coordinate: from \(y = 0\) (for a point on A) to \(y=-2\) (approximate for a corresponding point on B), the change in \(y\) is \(0-(-2) = 4\) units down.

Step2: Analyze other options

• Dilation: Dilation changes the size of the figure. Since polygon A and B have the same size (corresponding side lengths are equal), dilation is not involved.
• Reflection: Reflection over x - axis (horizontal reflection) changes the \(y\) - coordinate sign (\((x,y)\to(x, - y)\)) and reflection over y - axis (vertical reflection) changes the \(x\) - coordinate sign (\((x,y)\to(-x,y)\)). The orientation of polygon B with respect to A is not a result of reflection (as reflection would flip the figure in a mirror - like way, but here it's a shift).
• Rotation: Rotation \(180^{\circ}\) would change the position of the figure in a rotational sense (\((x,y)\to(-x,-y)\)), but combined with reflection, it does not match the simple shift from A to B.

Answer:

Translate 5 units right and 4 units down.